A Continuous Two-Dimensional Model of Threshold Learning

We present a model of threshold learning that represents discrete one-dimensional learning processes by a continuous two-dimensional learning process. The model gives us an overall view of the learning dynamics of an expanded range of training procedures, and provides insight into the training of multidimensional linear pattern classifiers. In our model the expected performance is measured by learning curves, and the confidence in this expected performance is measured by variance curves. Previous work on the continuous approximation has been restricted to one-dimensional learning processes. The theory developed here promises to lead to improved training procedures and improved rules for determining when to stop training.